Fun with Pascal's Triangle
Students will be able to recognize and reproduce the integers, rows and columns of number patterns that make up the Pascal Triangle.
How it works:
Step 1: Tell the students that the rows and columns of integers that make up the triangle known as "Pascal's Triangle". Ask the students to look at Pascal‘s Triangle and find the many number patterns.
Step 2: Display Pascal’s Triangle chart on smart board or chart showing rows and columns of numbers via the overhead projector. Explain to the students that each row in the triangle begins and ends with the integer 1 and the inner numbers are always the sum of the two integers above it.
Step 3: Have students place Post-it® Notes in the formation of Pascal’s Triangle. Once the students show that they recognize this first pattern, show them that the numbers in alternating rows form columns that must be lined up under each other as the triangle is symmetrical.
Step 4: Discuss with the students that the sum of each two successive integers in the row above it is equal to the integer in the row below it and centered between the two integers.
Step 5: Have the students work in pairs trying to duplicate the Pascal’s Triangle using Post-it® Notes. One student looks a copy of Pascal’s Triangle while the other student tries to duplicate Pascal's Triangle. Students take turns showing covered missing numbers.
Step 6: The students use the Post-it® Notes to make his/her triangle after the lesson without referring back to the original triangle.
Assignment: Students can be shown how to identify some of the patterns in Pascal's Triangle and duplicate the triangle in a single lesson. They can then be encouraged to look for some of the many other patterns that exist in the triangle. Students can explore on their own.